A basketball coach ends every practice with a free throw dri

A basketball coach ends every practice with a free throw drill in which he requires each player to sink [11] free throws. Suppose one player has free throw percentage [47] %.

(a) What is the probability that it takes him exactly [51] tries to complete the drill?

Solution

Has to make 11 free throws and miss the remaining 40 of them

p = P(free throw) = 0.47

1 - p = P(does not make the free throw) = 1 - 0.47 = 0.53

P(x = 51, r = 11) = n C r * (p)^r * (1 - p)^(x - r)

(51C11) * (0.47)^11 * (0.53)^(40)

0.000110142640472816463896615265438655494597335502487 ---> ANSWER